Current status: Information processing with different types of chemical media has been studied for a long time. It is expected that chemical information processing devices can be reduced to nano-scale & work autonomously. Therefore, chemical computers seem to fit specific applications like intelligent nano-materials, smart drugs or deep space sensors where mass, and size reduction is crucial. Typical chemical information processing devices are constructed as networks of communicating nonlinear elements. There are many factors, e.g. character of nonlinear medium, type of communication or the geometry of interactions between processing elements that should be taken into account to design a device performing a specific function. Currently, chemical information processing devices are constructed with bottom-up approach: simple elements (e.g. logic gates) are invented & more complex operations are realized by concatenation of simple operations. We plan to develop algorithms that can optimize a selected complex structure of communicating nonlinear elements in order to achieve its max. functionality with respect to a specific information processing task. Inspiration for this PhD topic comes from the publications co-authored by J. Gorecki and P. Dittrich (Phil. Trans. R. Soc. A 373 (2015) 20140219;, International Journal of Neural Systems, 25, (2015), 1450032).

The goal: To write evolutionary algorithms that optimize the functionality of a given network of communicating chemical nonlinear elements for a specific information processing task.

Our approach: The project is multidisciplinary and covers: the evolutionary algorithms, information theory, theory of nonlinear processes, chemical kinetics & computer simulations of nano-scale systems with complex chemical reactions. Bearing in mind the problem complexity, we would like to apply the evolutionary algorithms to the automatic design. The fitness function optimized within the evolution will measure the mutual information between the system evolution and the expected answer of the device.

2

Effect of fluctuations in biological processes confined in nanoscale organs

Bogdan Nowakowski

Annie LemarchandUniversity Pierre and Marie Curie, France

Current status: The influence of fluctuations in biological systems has become a subject of intensive investigations since the rapid development of bioengineering and biochemical processing. Internal fluctuations may be an especially important issue in biological processes which are often restricted to nanoscale domains, where intrinsic stochastic perturbations reach a relatively higher level. Moreover, biochemical reactions are governed - as a rule - by nonlinear dynamics, which is particularly sensitive to even small perturbations of the average, deterministic evolution. In development processes, like genetic reproduction or cell differentiation, minor errors at the nanoscale are known to lead to significant phenotypical misexpressions. Inspiration for this PhD topic comes from the publication co-authored by B. Nowakowski and A. Lemarchand in J Chem Phys., 137, 074107 (2012)) and from the publication of B. Nowakowski group (J Chem Phys., 141, 124106 (2014)).

The goal: The present study should analyse in detail the robustness of dynamics to random perturbations, with focus on possible occurrence of morphogenesis mutations and metabolism malfunctions.

Our approach: The study will include (i) a theoretical approach with approximate (possibly analytical) calculations, (ii) simulations at different description levels: from deterministic scale to particle scale through stochastic, mesoscopic scale. Selection of the systems should be done in collaboration with a bioengineering company.

3

Investigation of lateral distribution of components in biological membranes

Current status: Biological membranes are multicomponent two dimensional fluids. The phospholipids form a bilayer where many different components such as proteins or hydrocarbons are embedded. The behaviour of proteins in biological membranes is still not sufficiently understood. Biological functions of proteins may be modified by their local concentration. The shape of the membrane may depend on the local concentration of components but also the concentration of components may be influenced by the membrane curvature. Inspiration for these studies comes from the publication co-authored by W. Gozdz and A. Iglic in PLoS ONE 8(9) , e73941, (2013) and from publication of W. Gozdz group in J. Chem. Phys., 137(1), 015101, (2012).

The goal: To better understand the physics of multicomponent biological membranes, and to elucidate, how the distribution of different kinds of components influences membrane properties and biological functions, related to differences in the local concentration of components. To describe (experimentally and theoretically) the interaction of biological membranes with nanoparticles and nanostructured surfaces, with the possible application in biomedicine.

Our approach: We will construct and investigate free energy functionals where the geometry of the biological membrane will be taken into account. Such approach combines knowledge from: physics (statistical mechanics), mathematics (differential geometry), biology (lipid membranes & biological cells), material science (fabrication of nanostructures), and computer science (numerical minimization, low level programming).We plan the collaboration with a Slovenian company Sensum d.o.o. (www.hellotrade.com) on the automatic determination of blood cell shapes for diagnostic purposes.

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 711859.